One of conventional standards relating to data recorded on a compact disk (hereafter, a “CD”) is based on a sampling frequency of 44.1 [kHz] and a quantization bit rate of 16 bits. Thus, the size of digital data for a CD or the like is represented using 16-bit representations corresponding to the values of 1 through −1. That is to say, encoding is carried out by dividing the values of 1 to −1 by the number of values that can be represented by the quantization bit rate and determining 16-bit numerical values corresponding to the individual values resulting from division. Quantization for a CD is performed by dividing the values of 1 to −1 with the accuracy of the 15th power of 2 excluding a sign bit. That is to say, in general, 16-bit values from 0x7FFF to 0x8000 are related to the original values of 1 to −1 as shown in FIG. 11. When the quantization bit rate is 24-bit, 0x7FFFFF to 0x800000 correspond to 1 to −1, as also shown in FIG. 11.
FIG. 12 shows a configuration of a recording device for recording on a CD. As shown in the figure, to record on a CD 123, audio signals for right and left channels are converted to 16-bit digital signals by a 16-bit A/D converter 121. The digital signals are written on the CD 123 by writing means 122. When a maximum voltage that can be input to the A/D converter 121 is denoted as Vdd and an input voltage on the A/D converter 121 associated with an analog audio signal is denoted as Vin as shown in FIG. 15, a voltage corresponding to 16-bit 0x0001 is a value obtained by dividing Vdd by the 15th power of 2, and Vin is represented by a multiple of that value. In other words, the A/D converter 121 encodes an analog audio signal input thereto according to the equation below to convert it into a 16-bit digital signal. In the process, a small variation in voltage below a voltage equal to Vdd divided by the 15th power of 2 will be rounded. Also, when Vin=Vdd, the corresponding value is 0x8000, but because the MSB is a sign bit, the value is rounded to 0x7FFF.
[Formula 1]
Known devices that thus outputs rounded input data include a device described in Patent Document 1, for example. When outputting input data with resolution decreased to a quarter, for example, the device first sets the initial input data as a reference value, then rounds the input data by dividing the data by 4 and dropping or rounding off the remainder, and outputs the resulting data. For subsequent input data having a variation from the reference value smaller than 4, the device does not change output data, i.e., outputs the rounded reference value. When subsequent input data varies from the reference value by 4 or greater, the device replaces the output data with a value obtained by rounding that input data and also updates the reference value to that input data. In short, the device permits change of output data only when a variation equivalent to reduction in resolution is found in input data, thereby ensuring smooth variation in output data.
Patent Document 2 describes a technique for rounding z-bit input data to z/2-bit data. This technique determines which bits to remove for rounding according to bits being used.
FIG. 13 illustrates a basic configuration of a reproducing device for reproducing audio recorded on a CD. For reproduction, an audio signal recorded on CD 133 is read as 16-bit data via a servo mechanism 134 and converted to an analog signal in a 24-bit D/A converter 135. The analog signal passes through an amplifier and volume 136 to drive loudspeakers 137.
Digital Signal Processors (DSP) and D/A converters, which are recent digital-signal processing ICs, have improved bit precision and are mostly 24-bit as the D/A converter 135. To input 16-bit data from the CD 133 to the 24-bit D/A converter 135, it is necessary to convert the 16-bit data to 24-bit data. Accordingly, data from the CD 133 is converted to 24-bit data by using the data from the CD 133 as upper 16-bit data and adding zeros as lower 8 bits to make 24-bit data, as shown in FIG. 14. The figure shows 16-bit CD data corresponding to original values from 1 to −1 as well as 24-bit data after conversion for use in the D/A converter and/or a DSP.
Patent Document 1: Japanese Patent Application Laid-Open No. H05-35258
Patent Document 2: Japanese Patent Application Laid-Open No. 2007-280082